Import Toon Shaded Character to an outside program?
I cannot say for certain if it can or can't be done, but I would advise against it regardless. Unity comes with a few toon shaders that are fine for most cases and are guaranteed to work with the engine.

What you do instead is that you export the mesh object by itself and build the material you want for it inside Unity. You also assign the texture for it in Unity if your object has one.

If you feel you need more control over the toon shader, there are some solutions over at the Unity Marketplace you could try.